2 (b) Interactions between continuous and binary variables Y i = 0 + 1 D i + 2 X i + u i  D i is binary, X is continuous  As specified above, the effect on Y of X (holding constant D ) = 2 , which does not depend on D  To allow the effect of X to depend on D , include the “interaction term” D i  X i as a regressor: Y i = 0+ 1 D i + 2 X i + 3 ( D i  X i ) + u i